In this chapter, we provide RD Sharma Solutions for Class 10 Chapter 7 Statistics Exercise 7.1 for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Solutions for Class 10 Chapter 7 Statistics Exercise 7.1 pdf, free RD Sharma Solutions for Class 10 Chapter 7 Statistics Exercise 7.1 book pdf download. Now you will get step by step solution to each question.
| Textbook | NCERT |
| Class | Class 10 |
| Subject | Maths |
| Chapter | Chapter 7 |
| Chapter Name | Statistics |
| Exercise | 7.1 |
| Category | RD Sharma Solutions |
RD Sharma Solutions Class 10 Chapter 7 Statistics Exercise 7.1
Question 1.
Calculate the mean for the following distribution :
| X | 5 | 6 | 7 | 8 | 9 |
| f | 4 | 8 | 14 | 11 | 3 |
Solution:
Question 2.
Find the mean of the following data:
| X | 19 | 21 | 23 | 25 | 27 | 29 | 31 |
| f | 13 | 15 | 16 | 18 | 16 | 15 | 13 |
Solution:
Question 3.
If the mean of the following data is 20.6. Find the value of p. (C.B.S.E. 1997)
| X | 10 | 15 | p | 25 | 35 |
| y | 3 | 10 | 25 | 7 | 5 |
Solution:
Question 4.
If the mean of the following data is 15, find p. (C.B.S.E. 1992C)
| X | 5 | 10 | 15 | 20 | 25 |
| f | 6 | P | 6 | 10 | 5 |
Solution:
Question 5.
Find the value of p for the following distribution whose mean is 16.6.
| X | 8 | 12 | 15 | P | 20 | 25 | 30 |
| f | 12 | 16 | 20 | 24 | 16 | 8 | 4 |
Solution:
Mean = 16.6
Question 6.
Find the missing value of p for the following distribution whose mean is 12.58. (C.B.S.E. 1992C)
| X | 5 | 8 | 10 | 12 | P | 20 | 25 |
| f | 2 | 5 | 8 | 22 | 7 | 4 | 2 |
Solution:
Question 7.
Find the missing frequency (p) for the following distribution whose mean is 7.68.
| X | 3 | 5 | 7 | 9 | 11 | 13 |
| f | 6 | 8 | 15 | P | 8 | 4 |
Solution:
Question 8.
The following table gives the number of boys of a particular age in a class of 40 students. Calculate the mean age of the students
| Age (in years) | 15 | 16 | 17 | 18 | 19 | 20 |
| No. of students | 3 | 8 | 10 | 10 | 5 | 4 |
Solution:
Question 9.
Candidates of four schools appear in a mathematics test. The data were as follows :
| Schools | No. of Candidates | Average Score |
| I | 60 | 75 |
| II | 48 | 80 |
| III | Not available | 55 |
| IV | 40 | 50 |
If the average score of the candidates of all the four schools is 66, find the number of candidates that appeared from school III.
Solution:
Question 10.
Five coins were simultaneously tossed 1000 times and at each toss the number of heads were observed. The number of tosses during which 0, 1, 2, 3, 4 and 5 heads were obtained are shown in the table below. Find the mean number of heads per toss.
| No. of heads per toss | No. of tosses |
| 0 | 38 |
| 1 | 144 |
| 2 | 342 |
| 3 | 287 |
| 4 | 164 |
| 5 | 25 |
| Total | 1000 |
Solution:
Question 11.
The arithmetic mean of the following data is 14, find the value of k. (C.B.S.E. 2002C)
| X | 5 | 10 | 15 | 20 | 25 |
| f | 7 | k | 8 | 4 | 5 |
Solution:
Mean=14
⇒ 14 (24 + k) = 360 + 10k
⇒ 336 + 14k = 360 + 10k
⇒ 14k- 10k- 360 -336 24
⇒ 4k = 24
⇒ k= (frac { 24 }{ 4 }) = 6 4
Hence k = 6
Question 12.
The arithmetic mean of the following data is 25, find the value of k. (C.B.S.E. 2001)
| X | 5 | 15 | 25 | 35 | 45 |
| f | 3 | k | 3 | 6 | 2 |
Solution:
Mean =25
⇒ 25 (14 + k) = 390 + 15k
⇒ 350 + 25k= 390 + 15k
⇒ 25k- 15k = 390 -350
⇒ 10k = 40 ⇒ k = (frac { 40 }{ 10 }) = 4
Hence k = 4
Question 13.
If the mean of the following data is 18.75. Find the value of p.
| X | 10 | 15 | P | 25 | 30 |
| f | 5 | 10 | 7 | 8 | 2 |
Solution:
⇒ 460 + 7p = 32 (18.75)
⇒ 460 + 7p = 600
⇒ 7p = 600 – 460 = 140
⇒ p = (frac { 140 }{ 7 }) = 20
∴ p = 20
Question 14.
Find the value of p, if the mean of the following distribution is 20.
| X | 15 | 17 | 19 | 20 + p | 23 |
| f | 2 | 3 | 4 | 5p | 6 |
Solution:
⇒ 5p2 + 100p + 295 = 20 (15 + 5p)
⇒ 5p2 + 100p + 295 = 300 + 100p
⇒ 5p2 + 100p – 100p = 300 – 295
⇒ 5p2 = 5 ⇒ p2 = (frac { 5 }{ 5 }) = 1
⇒ P= ±1
P = -1 i s not possible
∴ p= 1
Question 15.
Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 50.
Solution:
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